The near-wall domain decomposition method (NDD) has proved to be very efficient for modeling near-wall fully turbulent flows. In this paper the NDD is extended to non-equilibrium regimes with laminar-turbulent transition (LTT) for the first time. The LTT is identified with the use of the $e^N$-method which is applied to both incompressible and compressible flows. The NDD is modified to take into account LTT in an efficient way. In addition, implementation of the intermittency expands the capabilities of NDD to model non-equilibrium turbulent flows with transition. Performance of the modified NDD approach is demonstrated on various test problems of subsonic and supersonic flows past a flat plate, a supersonic flow over a compression corner and a planar shock wave impinging on a turbulent boundary layer. The results of modeling with and without decomposition are compared in terms of wall friction and show good agreement with each other while NDD significantly reducing computational resources needed. It turns out that the NDD can reduce the computational time as much as three times while retaining practically the same accuracy of prediction.